Abstract The paper investigates the role of monetary authority in its control of real cash balances through money supply. If money demand in Nigeria is stable the Central Bank of Nigeria can predict the level of money supply and there will be no inflationary pressure in the economy. The empirical analysis of the study involves application of tests for co-integration and vector error correction model. A test of stability was also conducted. The variables of the study are real money demand function (MD), gross capital formation (GCF), interest rate (INT), inflation rate (INF), exchange rate (EXR), government expenditure (GEX) and openness of the economy (OPE)) and co-integration test revealed long run equilibrium relationship. In the long run, it was discovered that interest rate, INF and OPE have negative impact on MD while the impact of GCF, EXR and GEX on the other hand are positive on MD in Nigeria. In the short run, lag values of MD, GCF, INT and EXR have negative relationship with current MD while the impact of INF and OPE are positive. The test of stability shows that real money demand function in Nigeria is stable as neither the CUSUM nor the CUSUMSQ plots cross the 5 percent critical boundaries. The study recommended that there should be a clear cut distinction between short run and long run objectives as the monetary authority, for example, can use inflation to reduce the level of money demand in the long run and increase it in the short run.